Details

sample417.0ms

Algorithm

intervals

Results

212.0ms	78×	body	10240	exit
123.0ms	80×	body	1280	valid
43.0ms	59×	body	640	valid
15.0ms	84×	body	80	valid
9.0ms	27×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.5b	(sin (expm1 a))
39.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(sin (expm1 a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series152.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
63.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2933	264
4	5001	264

prune197.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	38	13	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	13	52

Merged error: 33.6b

Counts

52 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (expm1 a))
0.5b	(sin (expm1 a))
0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `sin-diff` `pow-prod-up` `expm1-udef`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

2.0ms	(sin (expm1 a))
2.0ms	(sin (expm1 a))
6.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series274.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (expm1 a))
58.0ms	(sin (expm1 a))
153.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify88.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	177	692
1	561	615
2	2431	575
3	5002	554

prune355.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	71	25	96

Merged error: 33.1b

Counts

96 → 25

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

6.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

series153.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
3.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify69.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	141	1004
1	436	877
2	1887	841
3	5001	804

prune501.0ms

Filtered

81 candidates to 58 candidates (71.6%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	70	11	81
Fresh	1	22	23
Picked	1	0	1
Done	0	1	1
Total	72	34	106

Merged error: 32.8b

Counts

106 → 34

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
39.8b	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 38

Calls

4 calls:

5.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

series160.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (* (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))))) (atan a)) a)
4.0ms	(fmod (atan2 (expm1 (* (* (* (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))))) (cbrt (sin (expm1 a))))) (atan a)) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	106	993
1	199	842
2	487	650
3	1638	623
4	5001	623

prune284.0ms

Filtered

50 candidates to 39 candidates (78.0%)

Pruning

40 alts after pruning (38 fresh and 2 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	2	30	32
Picked	0	1	1
Done	0	1	1
Total	44	40	84

Merged error: 32.6b

Counts

84 → 40

regimes546.0ms

Accuracy

0% (2.1b remaining)

Error of 33.7b against oracle of 31.7b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	70
1	26	70

end0.0ms

sample12.8s

Algorithm

intervals

Results

7.0s	2594×	body	10240	exit
3.8s	2256×	body	1280	valid
1.2s	1758×	body	640	valid
282.0ms	2768×	body	80	valid
256.0ms	778×	body	320	valid
104.0ms	436×	body	160	valid
6.0ms	3×	body	2560	valid
4.0ms	1×	body	5120	valid